Sagging Center Beam in my basement

I have an older post WW2 cape cod two story home.

Many of the floor joists have literally started to buckle, and i have a sagging center beam of three 2 x 10's across the whole of the house supported on two wooden 6 x 6 or 8 x 8 posts with concrete footers.

I was going to break out the jack hammer and cut some holes in the floor, dig out the dirt underneath and make new concrete posts into the ground and level it off into the floor that is already there. (5000 psi concrete mix)

I was then going to try the jack and steel posts into position to support the center beam.

Is this the right way to do this ?

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This probably means that the footings under them were incorrectly poured and the soil/aggregate under them was not compacted correctly. Some settling is okay but from your description its sounds like its too much. If it was me personally I would build a support wall on either side of the beam, remove it and put in and LVL beam with 1/4" plate steel in between each one (3 lvl's, 2 plates of steel. I would then dig out the existing support, and footings, put in new aggregate and compact it probably (not with an 8x8 hamp tamper) but a real compactor. Then pour new footings and install the posts and refinish the concrete floor.

Or you could do it like a some people and just install jack posts and let it be.

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I had a really hard time following your post, there seems to be a missing sentence or maybe a few words in there. From the description, it appears you have sagging joists, and you believe the joist problem is due to the center beam being undersized, or possibly improperly supported.

Before spending a dime actually trying to repair, you need to determine the full extent of the problems, and determine the cause. No point spending money fixing something that isn't broken. One good way to start is to accurately measure (to within 1/8 inch) the elevations of the tops of the support posts, and the elevation along the main beam. This can be done with a "water level", a laser level, or an optical level. Once the survey is complete, you will know how much sag you have, and where it is. A little sag is normal (say less than 1/2 inch), if you have more serious deflection you can then begin to evaluate why it is happening.

After completion of the survey, and the analysis of the results, you can make a reasonable assessment as to whether you need to jack up the beam, sister the beam, brace the beam, or replace it. You can do the same thing with the floor joists. Trying to analyze your situation without any data is futile, let alone coming up with a rational repair plan.

Wooden posts on concrete are notorius for slowly decaying over time at the floor level. Your first plan, as Daniel suggested, should be to get a level and see where your problem lies. Why cut holes in the floor, if the real problem is that the posts have rotted? Check the bottom level of the beam at the foundation wall, the posts and at points in between. You will undoubtedly have some amount of sag between the posts. Determine whether the span between the posts is correct. If it's too long, then you can determine whether to add more posts or if it's within spec, to jack up and just replace the existing.

Wooden posts on concrete are notorius for slowly decaying over time at the floor level. Your first plan, as Daniel suggested, should be to get a level and see where your problem lies. Why cut holes in the floor, if the real problem is that the posts have rotted? Check the bottom level of the beam at the foundation wall, the posts and at points in between. You will undoubtedly have some amount of sag between the posts. Determine whether the span between the posts is correct. If it's too long, then you can determine whether to add more posts or if it's within spec, to jack up and just replace the existing.

Also you might want to check and see if there are footings under those posts. If not then you may just poke through the slab with a new post

Thank you for all your input so far. I have 3 2x10 old fashioned cut beams put together across the center of the house, to make a large beam. These in turn, rest on each side of the foundation wall, with 2 posts to support them approximately 36 to 48 inches apart from each other and the outside walls. They are 6 x 6 posts that have concrete footings poured into the floor itself. I did notice that these posts seem to be either shrinking or bending and twisting in some sort of fashion.